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Relating phase field and sharp interface approaches to structural topology optimization

Published online by Cambridge University Press:  05 August 2014

Luise Blank ,
Harald Garcke ,
M. Hassan Farshbaf-Shaker  and
Vanessa Styles
Luise Blank
Affiliation:
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany. luise.blank@mathematik.uni-regensburg.de; harald.garcke@mathematik.uni-regensburg.de
Harald Garcke
Affiliation:
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany. luise.blank@mathematik.uni-regensburg.de; harald.garcke@mathematik.uni-regensburg.de
M. Hassan Farshbaf-Shaker
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany; Hassan.Farshbaf-Shaker@wias-berlin.de
Vanessa Styles
Affiliation:
Department of Mathematics, University of Sussex, Brighton, BN1 9QH, UK; v.styles@sussex.ac.uk
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Abstract

A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement.

Keywords

Structural topology optimizationlinear elasticityphase-field methodfirst order conditionsmatched asymptotic expansionsshape calculusnumerical simulations
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 4 , October 2014 , pp. 1025 - 1058
Copyright
© EDP Sciences, SMAI, 2014

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